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Simplifying 2(1 + -5r) + 3(6 + 7r) + 46 = 0 (1 * 2 + -5r * 2) + 3(6 + 7r) + 46 = 0 (2 + -10r) + 3(6 + 7r) + 46 = 0 2 + -10r + (6 * 3 + 7r * 3) + 46 = 0 2 + -10r + (18 + 21r) + 46 = 0 Reorder the terms: 2 + 18 + 46 + -10r + 21r = 0 Combine like terms: 2 + 18 = 20 20 + 46 + -10r + 21r = 0 Combine like terms: 20 + 46 = 66 66 + -10r + 21r = 0 Combine like terms: -10r + 21r = 11r 66 + 11r = 0 Solving 66 + 11r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-66' to each side of the equation. 66 + -66 + 11r = 0 + -66 Combine like terms: 66 + -66 = 0 0 + 11r = 0 + -66 11r = 0 + -66 Combine like terms: 0 + -66 = -66 11r = -66 Divide each side by '11'. r = -6 Simplifying r = -6
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